Love to Learn. Online.

Inside iversity

«Poor, sad-eyed stranger!» – this is how American author Mark Twain described the canvasser or the salesman. Why was he so sad and poor? Maybe because he had to solve the big problem of a travelling salesperson – “Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?”. Without the answer, we could not trade today.

A long time ago, this was an inconvenient difficulty not only for the canvasser, but also for the mathematicians. The travelling salesman problem was mathematically formulated in the 1800s by the Irish mathematician W.R. Hamilton and by the British mathematician Thomas Kirkman.

Up to this day, the issue is existent for postmen and travellers all over the world. The most convenient and profitable approach for a solution is graph theory.

Another issue is called the Seven Bridges of Königsberg, named by Leonard Euler in 1736, and it sounds more like a beautiful legend than a problem.

Königsberg in Prussia (now Kaliningrad, Russia), was set on both sides of the Pregel River, and included two large islands, which were connected to the rest of the city by seven bridges. The problem was to devise a walk through the city that would cross each of those bridges once and only once. The residents of the city always challenged visitors and travellers to see whether they could solve the problem. However, no one except Leonard Euler could find a way; not even the locals. Euler proved that the problem had no solution. He was able to find a rule, using which, it was easy to determine whether it is possible to pass through all bridges, without passing twice on either of them. Its negative resolution laid the foundations of graph theory. Euler wrote a paper about the The Seven Bridges of Königsberg and published it in 1736. It was the first paper about graph theory in history and the first page of the history of graph theory.

This is the history. Now, let’s take a look at pop culture. Labyrinths have featured prominently in pop culture for a long time. Starting from the myths of Theseus and Minotaur and ending with the dystopian science fiction action thriller “The Maze Runner”. Or do you remember the fourth movie about Harry Potter and his adventures in the labyrinth? And the “The Shining” by Stephen King? The labyrinth challenges the hero to find the right path to escape. The study of labyrinths is also connected to graph theory. If the protagonists knew the basics of graph theory, they might have found a faster way out in some cases.

What then is the graph theory?

Graph theory in mathematics means the study of graphs. Graphs are one of the prime objects of study in discrete mathematics. In general, a graph is represented as a set of vertices (nodes or points) connected by edges (arcs or line). Graphs are therefore mathematical structures used to model pairwise relations between objects. They are found on road maps, constellations, when constructing schemes and drawings. Graphs underlie many computer programs that make modern communication and technological processes possible. They contribute to the development of thinking, both logical and abstract. For example, maybe you remember this game from your childhood: connect the dots on the piece of paper to make a figure, a dog or a cat – those connections are also graphs.

We all know the saying: “Mathematics is not needed in real life”, but graph theory is actually applicable in real life. In fact, this is how it was discovered.

What the course is about

ITMO University in St. Petersburg, Russia, is a large state university and one of Russia’s National Research Universities. Research priorities of the university are concentrated on information and photonic technologies. The online course „Einführung in die Graphentheorie“ is focused on the study of methods and algorithms of graph theory and their application in practice. The goal of the course is to develop basic knowledge and skills to solve the most important and frequently encountered graph problems.

You will, first of all, gain a readiness to demonstrate a basic knowledge of mathematics (graph theory). And secondly, you will learn to apply effective methods and algorithms for solving typical graph problems in practice. Furthermore, this course will be very useful for all those, who encounter graph theory in university – either on a beginner level or for in-depth studies and research.

The course consists of four chapters and a final exam. The theory will be taught through video lectures. The length of our teaching videos is of the time it would take to teach the same material in a lecture setting. Therefore, each video lecture lasts about 15 minutes. After completion of each video lecture, an online quiz is conducted to verify the that you as a learner understand what has been taught.

The main goal of this course is to gain basic knowledge in graph theory. This knowledge will help you to independently study other sections of graph theory in the future, and to apply it in real life. Do note, however, Graph theory develops very quickly. There are various terms and concepts, the correct use of which is possible only in the context of the problem being solved.

As I have explained in my post on online student engagement, active online learning is key when it comes to motivating learners. What do I mean by active? An online course championing “active online learning” should prompt the learner to participate and contribute. One way of doing this is to inject small tasks into learning videos, another common approach is ordinary multiple choice.

For effective online learning to take place, however, online learning has to move beyond making learners dance to the instructor’s tune. Exercises (which are optional) and assignments (which are mandatory) should challenge learners to think for themselves and to come up with their own creative solutions to open-ended questions. Not just for a few moments, but often a few hours. Learners write essays, prepare presentations, work on designs, spreadsheet models and programming assignments. The idea is to enable, if not encourage, them to think outside the box. And to come up with their own (often unexpected) solutions.

For example, one student in the course Design 101 came up with a unique and very creative
solution to the following assignment: “Carefully choose a recipe to cook for yourself. Today, you cook your chosen recipe and share with us a picture of your starting ingredients. Nothing less, nothing more.” You would expect them to use ingredients and kitchen utensils as suggested, right? But this student decided to give the assignment her very own interpretation. She said I”m going to make pancakes. But my pancakes are going to be a bit different. They will be from felt.” Here you see the “ingredients” she decided to use as starting ingredients.

What this example illustrates is that the course – instead of simply telling people what a good and creative solution looks like – challenged the learner to think outside the box and come up with her own, brilliant solution. Active online learning should allow for precisely this kind of open-ended experimentation. Instead of simply making people regurgitate information and knowledge, learners should apply it in assignments. This leaves them with both the opportunity to fail as well as to succeed beyond expectation.

Making Active Online Learning Social: The Learning Journal

The next step is to embed these kind of assignments in a social context. In order to do this we have created the so-called Learning Journal. The Learning Journal is an individual course blog that learners can use to share their solutions for the various assignments, take notes and discuss their work with the course community. Learners can »follow« the journals of other users to keep track of new content created by those peers they think stand out from the crowd.

Different layers of privacy settings allow learners to share their posts with no one, other participants in the same course or publicly on the internet. Through public sharing, journals can function as learning portfolios. These serve as public, linkable proof of the things learners have created and accomplished in a course.

The course journal aggregates the journal posts from all users in the course. Learners can “like” each other’s work simply by clicking on the heart. Of course they can also leave more substantial feedback in prose. The hearts as well as the comments can be used to identify quality in quantity. Learners can also sort their posts either by date (starting with the most recent uploads) or by “most liked”. To easily navigate through specific assignments users can also filter by unit or search for the work of a specific learner.

2017 is off to a fresh start and so is the iversity blog. After quite a long break we decided that we should give it a new focus. A focus that will be the same as our new motto: « Love to learn. Online. » Surprise, surprise – it’s all about online learning you will love.

In the past, our posts have covered a broad variety of aspects of online learning as well as course topics. As a consequence, the blog had something for everyone, but wasn’t geared towards anyone in particular. We want to take a more focused approach, true to our new motto «Love to Learn. Online.» Going forward, this blog will investigate what makes online courses an experience you love.

In the last five years, I have travelled all over the world attending scores of conferences in over a dozen countries on three different continents in order to learn about the future of learning. I will draw on the knowledge and connections I have gained during this time, as well as on the book “The University in the 21st Century” that I co-authored with Yehuda Elkana. It was published originally in 2012 in German and as a revised edition in English in 2016.

The following presentation that I gave at the TEGEP Summit in Istanbul in November 2016 gives you a glimpse of much of the material that I will cover in significantly more depth over the coming weeks:

If You Love to Learn: Join the Conversation!

Post topics will range from the conceptual thinking behind our instructional design to course production techniques; from platform features and our UX-philosophy to course case studies; from expert guest contributions to interviews with instructors and other iversity team members.

We want to engage in a reciprocal and mutually beneficial conversation with learners, instructors, corporate L&D experts, bloggers, journalists, learning psychologists, and other learning researchers. Whether you already use (and hopefully love) our courses, or you just stumbled upon this page, we would like your input to help us create online courses you love. Please leave a comment or send us an email if you have something you would like to share!
In short: we want to make this blog one of the best and most useful resources out there on fun and effective online learning.

Oh, and since I just mentioned sharing: of course we would be delighted if you decide to share our posts and the insights you have gained reading them with your network by email, in online social networks (yes, LinkedIn counts!) or even by the coffee machine.

Do you enjoy learning at iversity? Then recommend us to your friends and get rewarded for it! With our Spring Rewards Programme (15 March – 15 April) for each purchase your referred friends make, we’ll give 10% of the purchase value back to you. Are you taking a course you really like? Are there courses you would like to recommend to your friends? Not only is learning more motivating and fun with friends, you can enjoy a little something extra this Spring.

How can I participate in the Spring Rewards Programme?

Invite your friends to a course by sharing your personal referral link. Just go to your My Referrals page, found in the drop down menu in the top right corner, under your login name. Here you can find all the information about the Spring Rewards Programme, an overview of all courses you can refer and your corresponding personal referral links. Which courses would you like to recommend to your friends? To invite your friends, send them your unique referral links next to the courses or share them by using the social media buttons. Remember: Only when your friends enrol via these links, can we attribute them to your iversity account. If you would like to know more about referrals, please visit the FAQs at the bottom of your My Referrals page. Continue reading Spring Rewards Programme: Invite Friends, Earn Rewards

Let’s stay in touch

Categories

Blog Newsletter

Email Address*

First Name

Last Name

* = required field

About iversity

iversity.org is an education platform that offers online courses in collaboration with universities, companies and NGOs. The company, originally founded in 2011, was the first European platform to offer Massive Open Online Courses (MOOCs) as well as the first platform globally that offered courses awarding ECTS credits. Today iversity has over 750,000 users and more than one million course enrolments. Since entering the B2B business in 2015 a number of blue-chip clients have decided to adopt the iversity corporate learning solution.